Average Error: 29.6 → 0.0
Time: 1.3s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\mathsf{hypot}\left(re, im\right)\]
\sqrt{re \cdot re + im \cdot im}
↓
\mathsf{hypot}\left(re, im\right)
double f(double re, double im) {
        double r843188 = re;
        double r843189 = r843188 * r843188;
        double r843190 = im;
        double r843191 = r843190 * r843190;
        double r843192 = r843189 + r843191;
        double r843193 = sqrt(r843192);
        return r843193;
}
↓
double f(double re, double im) {
        double r843194 = re;
        double r843195 = im;
        double r843196 = hypot(r843194, r843195);
        return r843196;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.6

    \[\sqrt{re \cdot re + im \cdot im}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{hypot}\left(re, im\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{hypot}\left(re, im\right)\]

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))